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In this chapter we will study to find the surface area and volume of solid figure , like parallelepiped , cube, cuboid, cylinder , cone , frustum of cone , sphere and hemisphere and we will study to find the surface area and volume of combination of solid figures combination of two or more different or similar solid figures.

SOLID FIGURES
The objects which occupy space (i.e. they have three dimensions ) are called solids.
The solid figures can be derived from the plane figures.
e.g. In figure (i) , we have a paper cut in the form as shown. It is a plane figure. But when we fold the paper along the dotted lines, a box can be made as shown in figure (ii) , which occupies some part of the space. It has more than two dimensions and therefore it fulfils the criteria of being a solid figure.

Today we are going to study about rational expressions,
RATIONAL EXPRESSIONS
An expression of the form p(x) / q (x) , where p(x) and q(x) are polynomials and q(x) ≠ 0 is called a rational expression.
* In the rational expression p(x) / q(x) , p(x) is called the numerator and q(x) is called the denominator of the rational expression.
* Every polynomial can be said to be rational expression. Since p(x) can always be written as p(x) / 1 .
* Every rational expression need not be a polynomial .

Today we are going to learn about how the sequence of various numbers work and how we can trace out what number would follow after a certain number , or at a particular index,

PROGRESSION
Sequence following certain patterns are called progression.
e.g. 2,3,4,5,..... is a progression, here each term is interesting, here each term is increasing by 1.
ARITHMETICAL PROGRESSION
An arithmetic progression is a sequence in which the difference between any term and its just preceding term is constant through. The constant 'd' is called the common difference. The first term of AP is represented by 'a' and the formula for the xth term is aₓ = a + (x - 1) d

Let x be a rational number and n be a positive number such that ⁿ√x is irrational , then ⁿ√x is called a radical of order n or surd and here x is called the radicand.

* A surd of order 2 is called quadratic surd, i.e. √2
* A surd of order 3 is called a cubic surd i.e. ³√5
* A surd of order 4 is called a biquadratic surd
* A surd has no fraction under the radical sign .
* The radicand has no factor with exponent n.
* A surd is not equal to any surd of order lower than n.
* ⁿ√x is a surd only if x is a rational and ⁿ√x is irrational.
* When x is irrational or ⁿ√x is rational then ⁿ√x is not a surd.

Today we are going to study about the number system and how we can really play with the numbers.
NUMBER SYSTEM
The system of numeration employing then ten digits 0, 1,2,3,4,.....,8 ,9 is known as number system .
A group of digits, denoting a number is called a numeral.
A number may be a natural number , a whole number , an integer , a rational number , a real number etc.It is important to mention here that the above classification of numbers is not mutually exclusive, e.g. . An integer can also be a whole number or a natural number.

There is a saying , Mathematics gives you more analytics powers at hand .

This is quiet true . Today we are going to tell you about ,

5 CEOs who studied mathematics .
According to some reports by the Education Department of United States, the people who study mathematics or science have the highest rates of employment.

And also having a mathematics degree , gives you more significance .

According to some reports, jobs have grown 75% faster as because more and more math graduates were in the market and the students with such a degree were having a high probability of having a high paying job.

What are the best books for you to improve your mathematics,
There are various people and they have different needs of what they want to read about , actually there needs depend upon may be what they are presently pursuing or what they want others to read.
Here is my list of recommended best books for you to improve your mathematics , so that you may learn better .
I have divided the whole things into categories so that it may get easier for you to get an idea of what book you want .

HEIGHT AND DISTANCE -
Sometimes , we need to find the height of tower , building , tree , distance of a ship from light house, width of river and angle subtended by any object at a given point, etc.
We cannot measure them accurately , though we can find them using the concepts of ,
(1) Angle of elevation
(2) Angle of depression
ANGLE OF ELEVATION -
Angle of elevation is defined as an angle subtended by an eye with the horizontal axis to see an object in the upward direction.

This post is going to be deviating you from the topics of mathematics, but i am including this as because i got a lot of requests of how to do this ,
HOW CAN ONE APPROVE HIS / HER ADSENSE ACCOUNT IN JUST A FEW DAYS?
This question always trouble a lot of persons , when they seek Adsense approval for their new blogs.
They usually search on the internet on how to do it in only a few days.
And most of the times they are left empty handed.

So, in this post i am going to tell you guys how i got my Google Adsense in just 11 days from the very start of my blog .
Tips: Do follow what i am going to tell you guys in this blog post , really this will help you in a great way .

I am going to tell you the secrets that i did with my blog so that you may too get a Google Adsense account.

Do you want to learn something about linear equations and how to play with them?Here is your guide to it . Tips : grab a cup of coffee and enjoy this long article .so here we begin ,
EQUATION
An equation is a statement of equality of two algebraic polynomial(monomials) involving one or more variable.
or
An equation is a statement in which two algebraic expressions are equal.
e.g. 7x+5 = 0 is an equation but only 7x+5 is an expression.

How to learn locus ?What is a 'locus'?Why do we need to read about it? Here is your answer to every question in your head
LOCUS
The curve described by any point which moves under the given geometrical conditions is called locus.
e.g. The locus of a point (in a plane) equidistant from a fixed point (in a plane) is a circle with the fixed point as centre.
The plural of locus is loci and it is a read as losai.
* The locus may be a line or lines , straight or curve.
* Every point which satisfies the given geometrical conditions lies on the locus and vice versa.
* A point which does not satisfy the given geometrical conditions cannot lie on the locus and vice versa.

I hate long articles or blog posts , don't you ?That's why i write mine really very short, descriptive and covering all the concepts in one go .This post is regarding the hcf and lcm of polynomials and monomials. If you want to learn about the hcf and lcm of numbers then click this yellow link below . It will take you to another article . Sorry ;)HCF and LCM
HCF OF POLYNOMIALS
The highest common factor of two or more algebraic expressions is the factor of the highest degree which divides each of the expressions without a remainder.
It is denoted by HCF or GCD.
It is a convention to take HCF in such a way that the coefficient of the highest power of the variable is positive.

log ! log ! log!You know this was the most scary term in mathematics for me when i was in high school!But when i studied it , it became the most easy concept to learn and i used to do the problems in seconds . And sometimes that too without using pen and paper.
LOGARITHM
If 'a' is a positive real number other than 1 and 'b' is a rational number such that aⁿ= B then we say that logarithm of B to base 'a' is n or 'b' is the logarithm of N to base 'a', written as
logₐ B = n
So, aⁿ = B <=> log ₐ B = n
e.g. 7º = 1 <=> log ₇ 1 = 0

This blog post is going to tell you about polynomials , and if you want to learn them , then believe me that this is the right place for you . Great article coming up !Don't you believe me?you will ! :)
POLYNOMIALS
An algebraic expression having a variable x and its non-negative integral powers with real numbers as coefficients is called a polynomial in x.

So good to see you here !I think learning is the most valuable thing we can do to ourselves .I don't know i may be biased with studies, but i love it to do .Hope that you will digest this article and start loving the numbers :)
SQUARE OF A NUMBER
The square of a number is obtained by multiplying it by itself.
e.g. Square of 5 = 5 * 5 = 25 , square of 6 = 6 * 6 = 36
Perfect square or square number -
A natural number n is called a perfect square or a square number , if there exists a natural number m i.e. n = m².
e.g. The numbers 1 , 4 , 9 , 16 , 25 ,........ are square number.

I was always the first kid in my classroom to whom the teacher used to ask what percentage of studies do you do at home?And i was confused every time, why because i did not know the answer? Not really , i knew it .... but the answer was 0% .heheBut yeah of course i used to cover all this during the school hours of mine ,so , lets start this blog post and i hope this will help you guys learn at a much faster rate.
PER CENT
Per cent is a fraction whose denominator is 100 and numerator of the fraction is called the rate per cent . Per cent is denoted by the symbol '%'.

Tips: have a cup of tea ! i know you are going to love this .
RATIO
A ratio is the fraction or comparison of two or more quantities of the same type by division , i.e. if a and b are two quantities of same kind then the fraction a/b is called the ratio a to b . Here , a is called the first term (or antecedent) and b is called the second term (or consequent ) .
e.g. The ratio of 7m to 9m or 7 : 9.

How to study fractions ?Ever Wondered?This is where your search is going to end , not an end but this is where you are going to dive into the concepts of decimal fractions .
FRACTIONS-
A number which can be expressed in the form of p/q where q does not equal to 0 , is known as fraction .
e.g. 4/5 , 3/2 ,etc are fractions and here the lower number is called as denominator and the upper number is called as numerator.